Eco395 - assignment use the 95 confidence intervals for

Question

PART A-

1. Consider the following model that relates the proportion of a household's budget spent on alcohol WALC to total expenditure T OTEXP, age of the household head AGE, and the number of children in the household   NK.

WALC = β₁ + β₂ ln(TOTEXP ) + β₃AGE + β₄NK + e

A cross section sample of 1519 households were drawn from the 1980-1982 British Family Expenditure Surveys. Data have been selected to include only households with one or two children living in Greater London. Self-employed and retired households have been excluded. Note that only households with one or two children are being considered. Thus, NK takes only the values 1 or 2. Output from estimating this equation appears in Table 1 below.

Dependent Variable: WALC                                                                Included observations: 1519
Variable	Coefficient	Std. Error	t-Statistic	Prob.
C	0.0091	0.0191		0.6347
ln(TOTEXP)	0.0276		6.6086	0.0000
AGE		0.0002	-6.9624	0.0000
NK	- 0.0133	0.0033	-4.0750	0.0000
R-squared			Mean dependent var	0.0606
S.E. of regression			S.D. dependent var	0.0633
Sum squared resid	5.752896

(a) Fill in the following blank spaces that appear in this table.

i. The t-statistic for b₁.

ii. The standard error for b₂.

iii. The estimate b₃.

iv. R².

v. σˆ².

(b) Interpret each of the estimates b₁, b₃, and b₄.

(c) Compute a 95% interval estimate for β3. What does this interval tell you?

(d) Test the hypothesis that the budget proportion for alcohol does not depend on the number of children in the household. Can you suggest a reason for the test outcome?

(e) Compute the Adjusted R².

(f) Write out the estimated equation in the standard reporting format with standard errors below the coefficient estimates.

2. Professor Ray C.  Fair  has  for  a  number  of  years  built  and  updated  models  that explain and predict the U.S. presidential elections. See his website at https://fairmodel.econ.yale.edu/vote2008/index2.htm, and see in particular his paper entitled "A Vote Equation for the 2004 Election." The basic premise of the model is that the incumbent party's share of the two-party (Democratic and Republican) popular vote (incumbent means the party  in  power at the time of the election) is affected by  a number of factors relating to the economy and variables relating to the politics, such as how long the incumbent party has been  in  power  and  whether  the  President  is  running  for reelection.  Fair's data, 31 observations for the election years from 1880 to 2000, are in the file A4Q2.dta. The dependent variable is V OT E= percentage share of the popular vote won by the incumbent party. Consider the explanatory variable GROWT H = growth rate in real per capita GDP in the first three quarters of the election year (annual rate) and INFLATION = inflation rate in the first 15 quarters of the administration.  One would think that if the economy is doing well, and growth is high and inflation is low, the party in power would have a better chance of winning the election. Submit your Stata log file in your assignment or in the D2L dropbox.

(a) Estimate the regression model

VOTE = β₁ + β₂GROWT H + β₃INFLATION + e

Report the results in standard format.  Are the estimates for (β₂ and (β₃ significantly different from zero at a 10% significance level? Did you use one-tail tests or two-tail tests?   Why?

(b) Predict the percentage vote for the incumbent party when the inflation rate is 4and the growth rate is -4.

(c) Suppose that the inflation rate is 4% and the growth rate is -4%. Also assume that β₁ = b₁ and β₃ = b₃. For what values of β₂ will the incumbent party get the majority of the vote?  Using this range of values as the null hypothesis, test the hypothesis that the incumbent party will get the majority of the vote against the alternative that it will not.

In order to get reelected, President Willie B. Great believes it is worth sacrificing some inflation as long as more growth is achieved.

(d) Test the hypothesis that a 1 % increase in both GROWT H and INFLATION will leave VOTE unchanged against the alternative that VOTE will in- crease.

(e) Test the hypothesis that Willie will not get reelected against the alternative that he will get reelected when the growth rate is 4% and the inflation rate is 5%. (Carry out the test in terms of the expected vote E(VOTE) and use a 5% significance level.)

3. Data for the 8 year period, 1990 to 1997, was collected on 44 rice farmers in the Tarlac region of the Philippines,  on the tons of rice (P rod),  hectares of land planted (Area),  person days of labor (Labor),  and amount of fertilizer in kilograms (Fert).  The proposed production function is going to ignore the actual date and use the data as one sample. The data is in a file entitled A4Q3.dta. Submit your Stata log file in your assignment or in the D2L dropbox.

(a) Estimate the production function below:

ln(Prod_i) = β₁ + β₂ ln(Area_i) + β₃ ln(Labor_i) + β₄ ln(Fert_i) + e_i.

Report the results, comment on the estimates and the statistical significance of the estimates.

(b) Using a 1% level of significance, test the hypothesis that the elasticity of production with respect to land is equal to 0.5.

(c) Predict the rice production from 1 hectare of land, 50 person days of labor, and 100 kg of fertilizer.

(d) Your economic principles suggest that the farmer should continue of apply fertilizer as long as the marginal product of fertilizer, (∂Prod/∂Fert), is greater than the price of fertilizer divided by the price of output. Suppose that this price ratio is 0.004. For Fert = 100 and the predicted value of P rod found from part c, show that the farmer should continue to apply fertilizer as long as β₄ > 0.1242.

(e) Using a 5% level of significance, test the hypothesis that the elasticity with respect to land is equal to the elasticity of production with respect to labor.

(f) Test the hypothesis that the production function exhibits constant re- turns to scale, (H₀: β₂ + β₃ + β₄ = 1), at the 10% significance level.

(g) Using a 5% significance level, test the hypothesis that the mean of log output equals 1.5 when Area = 2, Labor = 100 and Fert = 175. State the null and alternative hypotheses in terms of β₁, β₂, β₃ and β₄.

PART B: DATA PROJECT

4. Create a log file and a do file of all the commands used in this exercise. You will need to submit both, the log file and the do file, into D2L.

(a) Regress the log of hourly wage on years of experience, age, and years of education,

ln(Wage) = β₁ + β₂Exp + β₃Age + β₄Educ + e.

(b) Report the results in standard form.

(c) Interpret the estimated coefficient on experience, (Exp).

(d) Comment on the signs and significance of the estimated coefficients.

(e) Test the overall significance of the model.

(f) Using the variable for gender, ECSEX99, estimate the same model for males only and estimate the model again for females only. Report the results in standard form.

(g) Compare and contrast the results from the three regressions.

(h) Test if the coefficient estimates for experience and education for males could take the estimated values you have for females.

(i) Use the 95% confidence intervals for females, for experience and education, to check if the estimated values for males are in the intervals. Do you get the same conclusions as in part h)?